Reconstruction and/or manipulation (generally, "reconstruction") of surface features of three-dimensional object(s) in a scene, from a plurality of two-dimensional images of the object(s), is useful in a number of applications. U.S. patent application Ser. No. 08/989,047, filed Dec. 11, 1997, in the names of Dan Albeck, et al., and entitled "Apparatus And Method For 3-Dimensional Surface Geometry Reconstruction" (hereinafter referred to as the "Albeck application") describes an apparatus for performing such reconstruction using a rig of three cameras, using a tensor arrangement described in U.S. patent application Ser. No. 08/497,224, filed Jun. 30, 1995, in the name of Amnon Shashua, and entitled "Apparatus And Method For Recreating And Manipulating A 3D Object Based On A 2D Projection Thereof" (hereinafter referred to as the "Shashua application") to generate information regarding reconstruction for the features of the object(s) from three images generated by the cameras. In the arrangement described in the Shashua application, the surface features that are reconstructed are defined by points that have coordinates in a coordinate system relative to one of the cameras in the rig. A problem arises in reconstruction if the surface features that are to be reconstructed cannot all be recorded by all of the cameras with the rig in one position. The apparatus described in the Albeck application provides a mechanism for moving the rig so as to allow the cameras to record sets of images of various portions of the surface(s) of the object(s). However, when the rig moves from one location, in which the cameras record a set of images of one portion of the object(s), to another location, in which the cameras record another set of images of another portion of the object(s), the coordinate system for the points defining the surface features of the various portions of the object(s) also changes.
In order to utilize the reconstruction information generated in the two coordinate systems in a unitary manner in connection with the object(s) in the scene, it is necessary to relate the coordinate systems to a common coordinate system, which will allow all of the points of the various portions of the reconstructed object(s) to be related to the common coordinate system, effectively "stitching" the reconstructions together. The common coordinate system can conveniently be one of the two coordinate systems used in reconstruction, or it can be a third coordinate system, but in any case all of the points for the various portions of the reconstructed object need to be related to a common coordinate system. When a rig, such as the rig described in the Albeck application is moved from one position to another, to facilitate recording of sets of images of different portions of the object(s), the movement comprises one or both of a translation and a rotation of the rig, both in three dimensions. If the translational and rotational movement of the rig can be controlled sufficiently precise, the relation of the coordinate system after movement to the coordinate system before movement can easily be determined. However, if, for example, the mass of the rig is sufficiently large, in a number of applications the movement of the rig cannot readily be controlled sufficiently precisely to allow sufficiently precise reconstruction.